** Unit description: **

The aim of this Research Unit is to present the state-of-the-art of control theory in what concerns systems governed by differential equations and systems. We consider optimal control and controllability questions both from the theoretical and numerical viewpoints.

In all cases, we assume that a system modeling the phenomenon under study (the state equation) is given. Some data in this system (the control variables) can be chosen more or less freely. In optimal control problems, the aim is to minimize a cost that depends on the solution of the model system (the state) and also on the control variables. In controllability theory, the aim is to choose the control in order to get the state we wish after a finite working time interval.

Usually, the main questions are: (a) Do “good” and “optimal” controls exist? (b) If yes, which is the cost (the effort) we have to pay to get these? (c) How can we compute them? We will try to provide answers (or partial answers) to these questions for many systems of different kinds. In most cases, open questions appear. Some of them have been selected as research projects for the students.

** Course program: **

- Optimal control for systems governed by ODEs and PDEs and its numerical approximation. Applications in Physics, Biology, etc.
- On the controllability of linear systems: The control of large systems with a small number of controls, boundary controllability of non-scalar systems, controllability and non-smooth data.
- Design of boundary control laws and observers using the backstepping method. Explicit results and numerical computation of control and observer kernels. Applications in Engineering.

** Lectures: **

- Enrique Fernández-Cara (Universidad de Sevilla)
- Manuel González-Burgos (Universidad de Sevilla)
- Rafael Vázquez (Universidad de Sevilla)

** Conference Speakers: **

- Anna Doubova (Universidad de Sevilla).
Title: "Some inverse problems with applications in Elastography: theoretical and numerical aspects".

Tuesday, April 10, 16:00 - 17:00.

Abstract (pdf). Slides of the talk (pdf)

** Schedule of the Course 2: **

- Thursday, April 5: 10:30-12:00 + 12:30-14:00 Manuel González Burgos.
- Friday, April 6: 10:30-11:30 (Manuel González Burgos) and 12:00-14:00 (Enrique Fernández Cara)
- Monday, April 9: 10:30-12:30 (Enrique Fernández Cara) and 12:30-13:30 (Rafael Vázquez)
- Wednesday, April 11: 10:00-11:30 and 11:30-13:30 (Rafael Vázquez)